fluid_mechanics

Problems 85
10 in.
1 ft
Cable
60°
Tie
Concrete
Form
10 ft
Water
Gate
6 ft 8 ft
Hinge
A
1 ft
F I G U R E P2.57
10 m
Hatch
Seawater
30°
Hinge
Air pressure, p 1
F I G U R E P2.58
Free surface
2.59 A long, vertical wall separates seawater from freshwater. If
the seawater stands at a depth of 7 m, what depth of freshwater is
required to give a zero resultant force on the wall? When the
resultant force is zero will the moment due to the fluid forces be
zero? Explain.
2.60 A pump supplies water under pressure to a large tank as
shown in Fig. P2.60. The circular-plate valve fitted in the short
discharge pipe on the tank pivots about its diameter A–A and is
held shut against the water pressure by a latch at B. Show that the
force on the latch is independent of the supply pressure, p, and the
height of the tank, h.
F I G U R E P2.61
in Fig. P2.61. Water acts against the gate which is hinged at point
A. Friction in the hinge is negligible. Determine the tension in the
cable.
†2.62 Sometimes it is difficult to open an exterior door of a
building because the air distribution system maintains a pressure
difference between the inside and outside of the building. Estimate
how big this pressure difference can be if it is “not too difficult”
for an average person to open the door.
2.63 An area in the form of an isosceles triangle with a base width
of 6 ft and an altitude of 8 ft lies in the plane forming one wall of
a tank which contains a liquid having a specific weight of
79.8 lbft 3 . The side slopes upward, making an angle of 60° with
the horizontal. The base of the triangle is horizontal and the vertex
is above the base. Determine the resultant force the fluid exerts on
the area when the fluid depth is 20 ft above the base of the triangular
area. Show, with the aid of a sketch, where the center of pressure
is located.
2.64 Solve Problem 2.63 if the isosceles triangle is replaced with
a right triangle having the same base width and altitude as the
isosceles triangle.
2.65 A vertical plane area having the shape shown in Fig. P2.65 is
immersed in an oil bath 1specific weight 8.75 kNm 3 2. Determine
the magnitude of the resultant force acting on one side of the
area as a result of the oil.
Pressure p
Supply
4 m 4 m
45°
h
Water
Oil bath
F I G U R E P2.65
A
B
A
F I G U R E P2.60
2.61 A homogeneous, 4-ft-wide, 8-ft-long rectangular gate weighing
800 lb is held in place by a horizontal flexible cable as shown
2.66 A 3-m-wide, 8-m-high rectangular gate is located at the
end of a rectangular passage that is connected to a large open
tank filled with water as shown in Fig. P2.66. The gate is hinged
at its bottom and held closed by a horizontal force, F H , located
at the center of the gate. The maximum value for F H is 3500 kN.
(a) Determine the maximum water depth, h, above the center
of the gate that can exist without the gate opening. (b) Is the
answer the same if the gate is hinged at the top? Explain your
answer.